Periodic orbits and Birkhoff sections of stable Hamiltonian structures
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866913513626140672 |
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| author | Cardona, Robert Rechtman, Ana |
| author_facet | Cardona, Robert Rechtman, Ana |
| contents | Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures on 3-manifolds: on one hand, we classify all the examples with finitely many periodic orbits under a non-degeneracy condition; on the other, we give sufficient conditions for the existence of a supporting broken book decomposition and for the existence of a Birkhoff section. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_14732 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Periodic orbits and Birkhoff sections of stable Hamiltonian structures Cardona, Robert Rechtman, Ana Dynamical Systems Symplectic Geometry Stable Hamiltonian structures generalize contact forms and define a volume-preserving vector field known as the Reeb vector field. We study two aspects of Reeb vector fields defined by stable Hamiltonian structures on 3-manifolds: on one hand, we classify all the examples with finitely many periodic orbits under a non-degeneracy condition; on the other, we give sufficient conditions for the existence of a supporting broken book decomposition and for the existence of a Birkhoff section. |
| title | Periodic orbits and Birkhoff sections of stable Hamiltonian structures |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2206.14732 |